The one-alarm fire was reported at 9:32 a.m. in an elevator shaft on the seventh floor of the building at 23rd Street and Potrero Avenue, spokeswoman Mindy Talmadge said.
The blaze was controlled at 10:18 a.m., she said.
Seven workers suffered smoke inhalation and one was taken to a hospital. A firefighter sustained a minor injury to her arm, Assistant Fire Chief Tom Siragusa said.
Hospital spokeswoman Rachael Kagan said the new building is slated to open at the end of 2015. She didn't yet know the extent of damage from the fire or whether it would affect that timeline.
However, Siragusa said he does not believe the damage will cause any significant delays to the project.
Kagan said this is the first problem that has occurred since construction started.
"We're very relieved no one was seriously hurt," she said.
The blaze did not affect hospital operations, Kagan said.
The fire prompted the closure of Potrero Avenue between 22nd and 24th streets. The street remained closed as of 10:40 a.m.
The cause of the fire is under investigation. Talmadge said crews were doing "hot work," or welding, in the shaft before the fire broke out.
The flames were confined to the shaft, Siragusa said.
California Division of Occupational Safety and Health has been notified about the fire, she said.